A quartic equation is an algebraic equation of the form
These types of equations are extremely hard to solve; however, there are very clever methods for solving them by bringing it down to a cubic. I am going to list the simplest of the five.
Solving Quartic Equations
Look in the "TLDR" section for the final result of each step.
Bringing it down to a depressed quartic
Start with the equation Divide both sides by a: Now, convert to a depressed quartic by substituting . You now have:
Now you have a depressed quartic: where , and .